In microfocus x-ray tubes, hairpin filaments are used where the wire is bent to a pointed tip to emit a fine electron beam in order to obtain a focal spot size in the pm range. However, due to increasingly higher tube currents and higher filament temperatures associated therewith, hairpin filaments have only a relatively short lifetime, and therefore the cathode needs to be replaced at regular intervals after a limited number of operating hours. Significant additional maintenance efforts and corresponding downtimes are thus caused, which constitutes an obstacle to the use of microfocus x-ray tubes in industrial manufacture.